Forward rates model and forward pricing model

CFA Level II
#1

[1+r(T*+T)]^(T*+T)=(1+r(T*)^T* (1+f(T*,T))^T

vs

P(T*+T)=P(T*)F(T*,T)

what are the relationship or difference between those two

For example, I have this question, calculate the forward price two year from now for a $1 par, 0 coupon and three year bond given S2=4% and S5=6%.

The answer used the second formula, but I wonder why is the first formula not right?I get really confused

#2

The relationship’s easy:

P(t) = 1/(1 + r(t))

Your equations say that:

  • The rate for T* + T equals the rate for T* compounded with the rate for T thereafter.
  • The current price for T* + T equals the price discounted for T*, then discounted again for T thereafter.

For the record, I think that CFA Institute’s notation for this is horrible: it confuses more people than it enlightens. A lot more.

#3

Now looking at it, I think what I messed up is one is calculating the ratel, the other, the one you laid out is price, theya re different things although you can get one from the other, is that right?

#4

Yes, that’s right.